Fire looks very low resolution
Under Intergration in the material for the smoke domain, decrease the Step Size and possibly also the Depth Cutoff. The step size determines how close together the volume calculations are, and decreasing it makes the render more accurate, but also slower. The depth cutoff sets the luminance below which to clamp to zero. Decreasing this also makes the render more accurate and slower.



This was rendered with the default settings, step size 0.100 and depth cutoff 0.010.



And this was rendered with values in the screenshot above, step size 0.02 and depth cutoff 0.005.



And as a side note (for if and when you decide to move to Cycles), in Cycles you change this under Volume Sampling in the render panel. The step size does the same as in Internal, but the depth cutoff has been replaced by Max Steps. This serves the same purpose, but with a different approach.